Acta Mechanica Solida Sinica

, Volume 29, Issue 1, pp 46–58 | Cite as

On Behaviors of Functionally Graded SMAs under Thermo-Mechanical Coupling

  • Bingfei Liu
  • Pengcheng Ni
  • Wei Zhang


An analytical solution is obtained for the Functionally Graded Shape Memory Alloy (FG-SMA) composites subjected to thermo-mechanical coupling. Young’s modulus and thermal expansion coefficient of the material are assumed to vary in different forms of power function through the thickness, with the Poisson’s ratio being constant. An SMA constitutive model is combined with the averaging techniques of composite to determine the mechanical properties of the FG-SMA composites. Different phase transformation steps and the corresponding stress distributions through the thickness direction are given. The results show that the average stresses decrease as the transformations proceed.

Key Words

functionally graded SMAs phase transformation constitutive model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aghababaei, R. and Joshi, S.P., Micromechanics of crystallographic size-effects in metal matrix composites induced by thermo-mechanical loading. International Journal of Plasticity, 2013, 42: 65–82.CrossRefGoogle Scholar
  2. 2.
    Eisenlohr, P., Diehl, M., Lebensohn, R.A. and Roters, F., A spectral method solution to crystal elasto-viscoplasticity at finite strains. International Journal of Plasticity, 2013, 46: 37–53.CrossRefGoogle Scholar
  3. 3.
    Chen, Y.L. and Ghosh, S., Micromechanical analysis of strain rate-dependent deformation and failure in composite microstructures under dynamic loading conditions. International Journal of Plasticity, 2012, 32–33: 218–247.Google Scholar
  4. 4.
    Liu, B.F., Dui, G.S. and Zhu, Y.P., A constitutive model for porous shape memory alloys considering the effect of hydrostatic stress. CMES-Computer Modeling in Engineering & Science, 2011, 78(4): 247–275.Google Scholar
  5. 5.
    Shabana, Y.M. and Noda, N., Thermo-elasto-plastic stresses in functionally graded materials subjected to thermal loading taking residual stresses of the fabrication process into consideration. Composites: Part B, 2001, 32: 111–121.CrossRefGoogle Scholar
  6. 6.
    Shao, Z.S. and Wang, T.J., Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal mechanical loads. International Journal of Solids and Structures, 2006, 43: 3856–3874.CrossRefGoogle Scholar
  7. 7.
    Wang, J.P., Chen, G. and Zhai, P.C., Creep property of functionally graded materials. Materials Science Forum, 2005, 492–493: 441–446.Google Scholar
  8. 8.
    Yin, H.M., Paulino, G.H., Buttlar, W.G. and Sun, L.Z., Effective thermal conductivity of two-phase functionally graded particulate composites. Journal of Applied Physics, 2005, 98: 063704.CrossRefGoogle Scholar
  9. 9.
    Chen, B. and Tong, L., Sensitivity analysis of heat conduction for functionally graded materials. Material Design, 2004, 25: 663–672.CrossRefGoogle Scholar
  10. 10.
    Guler, M.A. and Erdogan, F., Contact mechanics of graded coatings. International Journal of Solids and Structures, 2004 41: 3865–3889.CrossRefGoogle Scholar
  11. 11.
    Miyamoto, Y., Kaysser, W.A., Rabin, B.H., Kawasaki, A. and Ford, R.G., Functionally Graded Materials: Design, Processing and Applications. Dordrecht: KluwerAcademic Publishers, 1999.CrossRefGoogle Scholar
  12. 12.
    Benafan, O., Noebe, R.D., Padula II, S.A., Brown, D.W., Vogel, S. and Vaidyanathan, R., Thermomechanical cycling of a NiTi shape memory alloy-macroscopic response and microstructural evolution. International Journal of Plasticity, 2014, 56: 99–118.CrossRefGoogle Scholar
  13. 13.
    Yu, C., Kang, G.Z. and Kan, Q.H., Crystal plasticity based constitutive model of NiTi shape memory alloy considering different mechanisms of inelastic deformation. International Journal of Plasticity, 2014, 54: 132–162.CrossRefGoogle Scholar
  14. 14.
    Yu, C., Kang, G.Z., Kan, Q.H. and Song, D., A micromechanical constitutive model based on crystal plasticity for thermo-mechanical cyclic deformation of NiTi shape memory alloys. International Journal of Plasticity, 2013, 44: 161–191.CrossRefGoogle Scholar
  15. 15.
    Lagoudas, D.C., Hartl, D., Chemisky, Y., Machado, L. and Popov, P., Constitutive model for the numerical analysis of phase transformation in polycrystalline shape memory alloys. International Journal of Plasticity, 2012, 32–33: 155–183.Google Scholar
  16. 16.
    Morin, C., Moumni, Z. and Zaki, W., Thermomechanical coupling in shape memory alloys under cyclic loadings: Experimental analysis and constitutive modeling. International Journal of Plasticity, 2011, 27(12): 1959–1980.CrossRefGoogle Scholar
  17. 17.
    Liu, B.F., Dui, G.S. and Yang, S.Y., On the transformation behavior of functionally graded SMA composites subjected to thermal loading. European Journal of Mechanics A—Solids, 2013, 40: 39–147.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Miyazaki, E. and Watanabe, Y., Development of shape memory alloy fiber reinforced smart FGMs. Materials Science Forum, 2003, 423–425: 107–112.Google Scholar
  19. 19.
    Lester, B.T., Chenisky, Y. and Lagoudas, D.C., Transformation characteristics of shape memory alloy composites. Smart Materials & Structures, 2012, 20: 1–13.Google Scholar
  20. 20.
    Zheng, B., Xu, J. and Qi, M., Preparation of graded DLC film on TiNi SMA by plasma enhanced deposition and behavior of corrosion-resistance. Journal of Functional Materials, 2007, 38(1): 115–118.Google Scholar
  21. 21.
    Mahmud, A.S., Liu, Y.N. and Nam, T.H., Gradient anneal of functionally graded NiTi. Smart Materials & Structures, 2008, 17: 1–5.CrossRefGoogle Scholar
  22. 22.
    Qidwai, M.A., Entchrv, P.B., Lagoudas, D.C. and DeGiorgi, V.G. Modeling of the thermomechanical behavior of porous shape memory alloys. International Journal of Solids and Structures, 2001, 38: 8653–8671.CrossRefGoogle Scholar
  23. 23.
    Birnbaum, A.J. Satoh, G. and Yao, Y.L. Functionally grading the shape memory response in NiTi films. Journal of Applied Physics, 2009, 106(4): 043504-043504-8.CrossRefGoogle Scholar
  24. 24.
    Zhang, Y.P., Zhang, X.P. and Zhong, Z.Y., Fabrication, transformation and superelasticity behavior of NiTi memory alloy with large pore-size and gradient porosity. Aata Metallurgica Sinica, 2007, 43(11): 1221–1227.Google Scholar
  25. 25.
    Fu, Y.L., Du, H.J. and Zhang, S., Functionally graded TiN/TiNi shape memory alloy films. Materials Letters, 2003, 57: 2995–2999.CrossRefGoogle Scholar
  26. 26.
    Berrabah, H.M., Mechab, I., Tounsi, A., Benyoucef, S., Krour, B., Fekrar, A. and Adda Bedia, E.A., Electro-elastic stresses in composite active beams with functionally graded layer. Computational Materials Science, 2010, 48: 366–371.CrossRefGoogle Scholar
  27. 27.
    Zhong, Z. and Shang, E.T., Three dimensional exact analysis of a simply supported functionally gradient plate. International Journal of Solids and Structures, 2003, 40: 5335–5352.CrossRefGoogle Scholar
  28. 28.
    Pitakthapanaphong, S. and Busso, E.P., Self-consistent elastoplastic stress solutions for functionally graded material systems subjected to thermal transients. Journal of the Mechanics and Physics of Solids, 2002, 50: 695–716.CrossRefGoogle Scholar
  29. 29.
    Birman, V., Review of mechanics of shape memory alloy structures. Applied Mechanics Reviews, 1997, 50: 629–645.CrossRefGoogle Scholar
  30. 30.
    Xue, L.J., Dui, G.S. and Liu, B.F., Theoretical analysis of functionally graded shape memory alloy beam subjected to pure bending. Journal of Mechanical Engineering, 2012, 48(22): 40–45 (in Chinese).CrossRefGoogle Scholar
  31. 31.
    Zhao, Y., Taya, M., Kang, Y.S. and Kawasaki, A., Compression behavior of porous Ni-Ti shape memory alloy. Acta Materialia, 2005, 53: 337–343.CrossRefGoogle Scholar
  32. 32.
    Boyd, J.G. and Lagoudas, D.C., A thermodynamic constitutive model for the shape memory alloy materials. Part I. the monolithic shape memory alloy. International Journal of Plasticity, 1996, 12: 805–842.CrossRefGoogle Scholar
  33. 33.
    Qidwai, M.A. and Lagoudas, D.C., On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material. International Journal of Plasticity, 2000, 16: 1309–1343.CrossRefGoogle Scholar
  34. 34.
    Sepiani, H., Ebrahimi, F. and Karimipour, H., A mathematical model for smart functionally graded beam integrated with shape memory alloy actuators. Journal of Mechanical Science and Technology, 2009, 23: 3179–3190.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2016

Authors and Affiliations

  1. 1.Airport CollegeCivil Aviation University of ChinaTianjinChina
  2. 2.Sino-European Institute of Aviation EngineeringCivil Aviation University of ChinaTianjinChina

Personalised recommendations